Scholarlink

<p>In this work, we adapt our recent article [<CitationRef CitationID="CR1">1</CitationRef>] to the setting of Dirichlet boundary conditions. A key part is the study of the parabolic equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(a\partial _t w - \Delta w = f\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>w</mi> <mo>-</mo> <mi mathvariant="normal">Δ</mi> <mi>w</mi> <mo>=</mo> <mi>f</mi> </mrow> </math></EquationSource> </InlineEquation> with a rough coefficient <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(a\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>a</mi> </math></EquationSource> </InlineEquation>, homogeneous Dirichlet boundary conditions, and the special assumption <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\partial _tw \ge 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>w</mi> <mo>≥</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. We then apply it to prove existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lotka-Volterra reaction terms in three dimensions and Dirichlet boundary conditions, and to obtain estimates for solutions to reaction-diffusion systems modeling reversible chemistry (still when Dirichlet boundary conditions are considered).</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Hölder regularity of parabolic equations with Dirichlet boundary conditions and application to reaction-diffusion and reaction-cross-diffusion systems

  • 期刊论文

  • 发表日期：

    2026年3月7日

查看全文
  • Hector Bouton,
  • Laurent Desvillettes,
  • Helge Dietert

摘要

In this work, we adapt our recent article [1] to the setting of Dirichlet boundary conditions. A key part is the study of the parabolic equation \(a\partial _t w - \Delta w = f\) a ∂ t w - Δ w = f with a rough coefficient \(a\) a , homogeneous Dirichlet boundary conditions, and the special assumption \(\partial _tw \ge 0\) ∂ t w ≥ 0 . We then apply it to prove existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lotka-Volterra reaction terms in three dimensions and Dirichlet boundary conditions, and to obtain estimates for solutions to reaction-diffusion systems modeling reversible chemistry (still when Dirichlet boundary conditions are considered).